The tolerances provided in Oskar's post are a bit on the high side. 0.3 and 0.15 or 0.1 respectively will do.
Just to be perfectly clear, you are saying 0.3mm will do where Oskar/Eric state "3: All gaps that are pulled open need 0.4 mm clearance." And you are saying 0.15mm or 0.1mm will do where Oskar/Eric state "5: Pin-in-hole constructions need 0.2 mm gap at all side to assure smooth sliding/turning." Correct?
What about 0.2 and then use some super glue to hold it in? Trying to get it perfectly snug is troublesome, as you will be subjected to the randomness of printing: some will fit, others won't.
Or if you don't want to use superglue, it is possible to design some hooks that create a snap fit. I've done that on one of my Constrained Cube designs and also on the Multidodecahedron.
I'm working on the challenge Oskar gave me and the connection point I'm thinking of is the face center to the geared axis under it. I don't want to glue these together as this will be a kit designed to be taken apart and reassembled as a different puzzle. As for holding them together that isn't a problem. The face center will be screwed into the core and both the face center and the axis its connected to will rotate around the arm off the core that the screw is screwed into. Its just that as the face center drives the axis (or the other way around depending on which side of the puzzle is being turned) so I want to minimize slop. So what I'm after is the tightest tolerance I can use yet still be certain the piece will fit. If you are saying 0.1mm is enough to allow turning (case 5 above), I'm going to guess that 0.05mm may be enough in this case.